Determining the rheological properties of a fluid through a non-linear response

ABSTRACT

Techniques for determining rheological properties of a fluid include actuating a resonator disposed in a volume that contains a fluid sample to operate the resonator in the fluid sample at a predetermined actuation scheme; measuring at least one characteristic of the resonator based on the operation of the resonator in the fluid sample; comparing the at least one measured characteristic to a rheological model that associates characteristics of the fluid sample to one or more rheological properties; and based on the comparison, determining one or more rheological properties of the fluid sample.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority under 35 U.S.C. § 119 to U.S.Provisional Patent Application Ser. No. 62/957,556, filed on Jan. 6,2020, the entire contents of which are incorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates to systems and methods for determiningrheological properties of a fluid and, more particularly, determiningrheological properties of a fluid used in hydrocarbon exploration andproduction through a non-linear response of a mechanical resonator.

BACKGROUND

The oil industry uses fluids (for example, non-Newtonian fluids) for thedrilling, hydraulic fracturing, and production stimulation ofsubterranean wells. Chemical industries produce petroleum-derivedproducts in refining and chemical production process from such producedhydrocarbon fluids. Contamination, damage to fluids, or changes in thequality of products can manifest as a change in the rheologicalproperties of fluids used in these processes. In some cases, it may beimportant for fluids to remain within the design envelope of rheologicalproperties.

SUMMARY

In a general implementation, a method for determining rheologicalproperties of a fluid includes actuating a resonator disposed in avolume that contains a fluid sample to operate the resonator in thefluid sample at a predetermined actuation scheme; measuring at least onecharacteristic of the resonator based on the operation of the resonatorin the fluid sample; comparing the at least one measured characteristicto a rheological model that associates characteristics of the fluidsample to one or more rheological properties; and based on thecomparison, determining one or more rheological properties of the fluidsample.

In an aspect combinable with the general implementation, the resonatorincludes a mechanical resonator.

In another aspect combinable with any one of the previous aspects, themechanical resonator includes a piezoelectric crystal, a MEMS device, ora tuning fork.

In another aspect combinable with any one of the previous aspects,actuating the resonator includes actuating motion on the resonatorthrough one or more signals to induce harmonic or anharmonic motion.

In another aspect combinable with any one of the previous aspects, theone or more signals includes one or more capacitive, piezoelectric,magnetic, or optical signals.

Another aspect combinable with any one of the previous aspects furtherincludes actuating the resonator with an actuation protocol thatactuates the resonator in at least one of a steady state motion or atime-dependent motion.

In another aspect combinable with any one of the previous aspects, thetime-dependent motion includes at least one sequence of displacements ofthe resonator with at least one of a plurality of amplitudes orfrequencies.

In another aspect combinable with any one of the previous aspects,actuating the resonator with an actuation protocol includes inducing ameasurable change on a motion of the resonator based at least in partdue to one or more deformations in the fluid sample.

In another aspect combinable with any one of the previous aspects,measuring at least one characteristic of the resonator includesmeasuring at least one characteristic in a transduction domain thatprovides a measurable signal from the operation of the resonator.

In another aspect combinable with any one of the previous aspects,measuring at least one characteristic in a transduction domain thatincludes at least one of a capacitive, a piezoelectric, a magnetic, oran optical characteristic.

In another aspect combinable with any one of the previous aspects,measuring at least one characteristic of the resonator includesmeasuring at least one of a velocity or a displacement of amplitude orphase of the resonator in at least one of a time domain or a frequencydomain.

In another aspect combinable with any one of the previous aspects,comparing the at least one measured characteristic to a rheologicalmodel includes comparing at least one motion characteristic of theresonator to at least one of a mathematical model or a computationalmodel.

In another aspect combinable with any one of the previous aspects, theat least one of the mathematical model or the computational modelrelates a change in the at least one motion characteristic to at leastone of a deformation amplitude or a deformation rate induced in thefluid sample.

In another aspect combinable with any one of the previous aspects,actuating the resonator disposed in the volume that contains the fluidsample to operate the resonator in the fluid sample at the predeterminedactuation scheme includes actuating a mechanical resonator disposed inthe volume that contains the fluid sample to vibrate the mechanicalresonator in the fluid sample at a predetermined vibration protocol.

In another aspect combinable with any one of the previous aspects,measuring the at least one characteristic of the resonator based on theoperation of the resonator in the fluid sample includes measuring atleast one motion characteristic of the mechanical resonator based on anon-linear response of the mechanical resonator in the fluid sample.

In another aspect combinable with any one of the previous aspects,comparing the at least one measured characteristic to a rheologicalmodel that associates characteristics of the fluid sample to one or morerheological properties includes comparing the at least one measuredmotion characteristic to the rheological model that associates motioncharacteristics of the fluid sample to one or more rheologicalproperties.

In another aspect combinable with any one of the previous aspects,measuring the at least one motion characteristic of the mechanicalresonator includes measuring the at least one motion characteristic witha photodetector positioned to receive a reflected laser beam thatoriginates with a laser beam source and reflects from the vibratingmechanical resonator.

Another aspect combinable with any one of the previous aspects furtherincludes circulating the fluid sample into the volume during actuationof the resonator.

In another aspect combinable with any one of the previous aspects,determining one or more rheological properties of the fluid sampleincludes iteratively determining the one or more rheological propertiesof the fluid sample with a numerical inversion or optimization protocol.

In another aspect combinable with any one of the previous aspects, theone or more rheological properties includes at least one of a complexviscosity, a storage modulus, a loss modulus, an apparent viscosity, aflow index, or a consistency factor of the fluid sample.

In another aspect combinable with any one of the previous aspects, therheological model includes at least one of a Bingham Plastic model, apower law model, a Hershel-Bulkley model, or a Carreau model.

In another aspect combinable with any one of the previous aspects, thefluid sample includes a non-Newtonian liquid.

In another aspect combinable with any one of the previous aspects, thenon-Newtonian liquid includes a hydrocarbon liquid, a completion liquid,or a petroleum-derived liquid.

Another general implementation includes a rheological propertymeasurement system that includes a container that includes a volume thatencloses a fluid sample; a resonator disposed within the volume and incontact with the fluid sample; a detector positioned to measure at leastone characteristic of the resonator based on an operation of theresonator in the fluid sample; and a control system communicably coupledto at least the resonator and the detector. The control system isconfigured to perform operations including actuating a resonatordisposed in a volume that contains a fluid sample to operate theresonator in the fluid sample at a predetermined actuation scheme;measuring at least one characteristic of the resonator based on theoperation of the resonator in the fluid sample; comparing the at leastone measured characteristic to a rheological model that associatescharacteristics of the fluid sample to one or more rheologicalproperties; and based on the comparison, determining one or morerheological properties of the fluid sample.

In an aspect combinable with the general implementation, the resonatorincludes a mechanical resonator.

In another aspect combinable with any one of the previous aspects, themechanical resonator includes a piezoelectric crystal, a MEMS device, ora tuning fork.

In another aspect combinable with any one of the previous aspects, theoperation of actuating the resonator includes actuating motion on theresonator through one or more signals to induce harmonic or anharmonicmotion.

In another aspect combinable with any one of the previous aspects, theone or more signals includes one or more capacitive, piezoelectric,magnetic, or optical signals.

In another aspect combinable with any one of the previous aspects, thecontrol system is configured to perform operations further includingactuating the resonator with an actuation protocol that actuates theresonator in at least one of a steady state motion or a time-dependentmotion.

In another aspect combinable with any one of the previous aspects, thetime-dependent motion includes at least one sequence of displacements ofthe resonator with at least one of a plurality of amplitudes orfrequencies.

In another aspect combinable with any one of the previous aspects, theoperation of actuating the resonator with an actuation protocol includesinducing a measurable change on a motion of the resonator based at leastin part due to one or more deformations in the fluid sample.

In another aspect combinable with any one of the previous aspects, theoperation of measuring at least one characteristic of the resonatorincludes measuring at least one characteristic in a transduction domainthat provides a measurable signal from the operation of the resonator.

In another aspect combinable with any one of the previous aspects, theoperation of measuring at least one characteristic in a transductiondomain that includes at least one of a capacitive, a piezoelectric, amagnetic, or an optical characteristic.

In another aspect combinable with any one of the previous aspects, theoperation of measuring at least one characteristic of the resonatorincludes measuring at least one of a velocity or a displacement ofamplitude or phase of the resonator in at least one of a time domain ora frequency domain.

In another aspect combinable with any one of the previous aspects, theoperation of comparing the at least one measured characteristic to arheological model includes comparing at least one motion characteristicof the resonator to at least one of a mathematical model or acomputational model.

In another aspect combinable with any one of the previous aspects, theat least one of the mathematical model or the computational modelrelates a change in the at least one motion characteristic to at leastone of a deformation amplitude or a deformation rate induced in thefluid sample.

In another aspect combinable with any one of the previous aspects, theoperation of actuating the resonator disposed in the volume thatcontains the fluid sample to operate the resonator in the fluid sampleat the predetermined actuation scheme includes actuating a mechanicalresonator disposed in the volume that contains the fluid sample tovibrate the mechanical resonator in the fluid sample at a predeterminedvibration protocol.

In another aspect combinable with any one of the previous aspects, theoperation of measuring the at least one characteristic of the resonatorbased on the operation of the resonator in the fluid sample includesmeasuring at least one motion characteristic of the mechanical resonatorbased on a non-linear response of the mechanical resonator in the fluidsample.

In another aspect combinable with any one of the previous aspects, theoperation of comparing the at least one measured characteristic to arheological model that associates characteristics of the fluid sample toone or more rheological properties includes comparing the at least onemeasured motion characteristic to the rheological model that associatesmotion characteristics of the fluid sample to one or more rheologicalproperties.

In another aspect combinable with any one of the previous aspects, theoperation of measuring the at least one motion characteristic of themechanical resonator includes measuring the at least one motioncharacteristic with a photodetector positioned to receive a reflectedlaser beam that originates with a laser beam source and reflects fromthe vibrating mechanical resonator.

In another aspect combinable with any one of the previous aspects, thecontrol system is configured to perform operations further includingcontrolling a pump to circulate the fluid sample into the volume duringactuation of the resonator.

In another aspect combinable with any one of the previous aspects, theoperation of determining one or more rheological properties of the fluidsample includes iteratively determining the one or more rheologicalproperties of the fluid sample with a numerical inversion oroptimization protocol.

In another aspect combinable with any one of the previous aspects, theone or more rheological properties includes at least one of a complexviscosity, a storage modulus, a loss modulus, an apparent viscosity, aflow index, or a consistency factor of the fluid sample.

In another aspect combinable with any one of the previous aspects, therheological model includes at least one of a Bingham Plastic model, apower law model, a Hershel-Bulkley model, or a Carreau model.

In another aspect combinable with any one of the previous aspects, thefluid sample includes a non-Newtonian liquid.

In another aspect combinable with any one of the previous aspects, thenon-Newtonian liquid includes a hydrocarbon liquid, a completion liquid,or a petroleum-derived liquid.

Implementations according to the present disclosure may include one ormore of the following features. For example, implementations accordingto the present disclosure may determine rheological properties of afluid sample with minimally invasive and localized measurements, unlikeconventional techniques which are either based on fixed fluiddeformation rates that give no information about rheology or requirecumbersome probes such as rotational rods driven by torque calibratedmotors. As another example, implementations according to the presentdisclosure may determine rheological properties of complex fluids, suchas refining process fluids, drilling fluids, and other hydrocarbonfluids, in which non-linear rheological measurements as described inthis disclosure provide more rich information about structural changesin the fluid than steady rotational, capillary and other conventionalrheological measurements. As another example, implementations accordingto the present disclosure may determine rheological properties byexploiting non-linear damping characteristics rather than focusing onlyon calculating a complex viscosity from the hydrodynamic force equationto obtain the viscoelastic properties of the fluid from the storage andviscous modulus.

The details of one or more implementations of the subject matterdescribed in this disclosure are set forth in the accompanying drawingsand the description. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example implementation of a rheologicalproperty measurement system according to the present disclosure

FIG. 2 is a schematic illustration of an example implementation of arheological property measurement system according to the presentdisclosure.

FIG. 3 is flowchart that describes an example implementation of a methodfor determining rheological properties of a fluid sample according tothe present disclosure.

FIG. 4 is a graph that illustrates an example of linear dependence ofmeasured current as a function of excitation amplitude in a mechanicalresonator that is used in the method of FIG. 3 .

FIG. 5 is a graph that illustrates optically detected resonance peaksfor a mechanical resonator immersed in a fluid sample during anexperiment according to the method of FIG. 3 .

FIG. 6 is a graph that illustrates peak amplitude at resonance for themechanical resonator immersed in the fluid sample during the experimentaccording to the method of FIG. 3 .

FIG. 7 is a schematic illustration of a controller or control system fora fluid rheology measurement system according to the present disclosure.

DETAILED DESCRIPTION

In example implementations, a rheological property measurement systemmay make inline measurement of rheological properties of fluids (forexample, non-Newtonian fluids), which properties are often important tomonitor during processes and to check for purposes of quality control.For example, the rheological property measurement system may determineproperties of fluids used in the upstream oil industry such as fluidsfor drilling, hydraulic fracturing, and production stimulation ofsubterranean wells. Example implementations of the rheological propertymeasurement system may also determine properties of fluids used in adownstream or chemicals industry, such as petroleum-derived products inrefining and chemical production. Because contamination, damage tofluids, or changes in the quality of products can manifest as a changein the rheological properties of these fluids during their handling,example implementations of the rheological property measurement systemmay eliminate or help eliminate such changes through the implementationof an inline and real-time measurement system.

Example fluids that may be measured by the rheological propertymeasurement system include drilling mud, hydraulic fracturing fluids,and polymers injected into reservoirs for enhanced oil recovery, forexample, during usage of such fluids in an upstream recovery process.Many of these fluids are considered non-Newtonian and, thus, theirproperties may be carefully designed for optimal performance. However,during operations, contamination or damage to the fluids may occur suchthat they no longer have the intended properties.

The functionality of drilling muds and other wellbore fluids such asfracturing fluids and enhanced recovery polymer fluids is introducedthrough design of the non-Newtonian characteristics of the fluid. Theviscosity dependence on shear and the solid-like properties of the fluidare used, for instance, to keep drill cuttings suspended while the fluidis static during a drilling operation. To maintain the desiredproperties of the fluid, it may be preferable to have constantinspection of the viscosity and density of the fluid (at the veryleast). However, due to the non-Newtonian properties of these fluids(shear dependent viscosity) full rheological characterization of suchfluids is also desirable and may be determined by the exampleimplementations of the rheological property measurement system.Furthermore, real-time measurement of these properties with therheological property measurement system described in the presentdisclosure may allow better optimization and automation of theoperations that use these fluids (for example, drilling, production).

FIG. 1 is a block diagram of an example implementation of a rheologicalproperty measurement system 100. As illustrated, the system 100 includesa fluid sample 125 and a resonator 105 (for example, a mechanicalresonator, also called a “sensor” in some aspects). In this example, theresonator is in contact with the fluid sample 125, which may be, forexample, a non-Newtonian fluid. For example, in some aspects, theresonator 105 is immersed in the fluid sample 125 (for example, within apipeline, container, or other enclosure).

System 100 also includes an actuator 115 that is communicably coupled tothe resonator 105. The actuator 115 may be operated to cause motion ofthe resonator 105 within the fluid sample 125, for example by applying aforce or displacement to the resonator. In some aspects, a particularsequence of forces or displacements, called an actuation scheme, may beapplied by the actuator 115 acting on the resonator 105 in order toproduce motion of the resonator within the fluid sample 125.

In the illustrated example of system 100, a detector 120 is alsocommunicably coupled with the resonator 105. The detector 120, forexample, is positioned (for example, within or external to the fluidsample 125) to detect dynamics, such as motion, strains, or stresses, ofthe resonator 105 during operation of the system 100. The motion of theresonator 105 in response to the actuation scheme may be changed oraffected by one or more fluid properties of the fluid sample 125, andmeasured by the detector 120.

System 100 also includes a control system (or controller) 110 that iscommunicably coupled to the actuator 115. The controller 110, in thisexample, may provide a human-machine interface for an operator of thesystem 100 to operate the actuator 115 to initiate a particularactuation scheme of the resonator 105.

In an example operation of system 100, a human-operator may operate thecontroller 110 to control the actuator 115 to apply a certain sequenceof motions or forces to the resonator 105. For example, the controller110 can control the actuator 115 to apply to the resonator 105 apre-determined sequence (for example, according to a known or pre-setactuation scheme) or a unique sequence of displacements, strains,forces, or stresses. The resonator 105 can then move within the fluidsample 125 in response to the actuation scheme and influenced by therheological properties of the fluid sample 125. The dynamics of theresonator 105 in response to the actuation scheme will be sensed by thedetector 120. The detector 120 can sense the dynamics of the resonator,converting these dynamics to a measurable signal output. In someaspects, the measurable output is provided (for example, to thecontroller 110) which determines one or more fluid properties of thefluid sample 125 based on measured characteristics of the detectoroutput in response to the actuation scheme. For example, the fluidproperties can be rheological properties, such as a complex viscosity, astorage modulus, a loss modulus, an apparent viscosity, a flow index, ora consistency factor.

As described, the actuator 115 can initiate operation of the resonator105 with a particular, pre-determined actuation scheme. Some exampleschemes include a sinusoidal excitation, other periodic excitationwaveforms, a non-periodic excitation such as a pulse, impulse, or stepexcitation, the parametric sweep technique, a multi-parametricactuation/detection technique, or the ring-up/ring-down technique, wheremeasurement of the decay envelope of the vibrations is performed whilethe actuation is switched on and off. The parametric study, for example,can operate the actuator 115 such that a particular factor is variedthrough a range of values during the operation, while all other factorsof the operation are held fixed at a baseline value. Each factor can bevaried through a range, in turn, while the other operational factors maybe held at a baseline. For example, the actuation force may be variedthrough a range of values so that a range of different oscillationamplitudes deform the fluid at different shear-rates, thus allowing theconstruction of a rheogram from the measured changes in the dampingforce (for example, viscosity) as a function of imposed shear-rates.

In some aspects, a non-Newtonian fluid can produce a non-linearrelationship between the detector signal and the actuator signal suchthat measurable characteristics of the detector signal produced by thenon-linear relationship to the actuator signal can be related torheological parameters of the non-Newtonian fluid. For example, in aNewtonian fluid, the detected amplitude of stress or motion of theresonator would be proportional to the motion or stress applied to theresonator by the actuator. In a non-Newtonian fluid, however, thisproportionality may not apply. For example, if a certain actuator motionproduced a certain detected force on the resonator, an actuator motionwhich is twice as large would produce a detected force which is twice aslarge in a Newtonian fluid, less than twice as large in a non-Newtonianshear-thinning fluid, and more than twice as large in a non-Newtonianshear-thickening fluid. Similarly, if a certain actuator force producesa detected resonator motion, then an actuator force twice as large wouldproduce twice the motion in a Newtonian fluid, more than twice themotion in a shear-thinning fluid, and less than twice the motion in ashear thickening fluid.

Accordingly, parameters of the shear-thinning or shear-thickeningrheological behavior of a non-Newtonian fluid can be obtained by anactuation scheme where sinusoidal signals of two or more differentamplitudes are applied in sequence to control the actuator and theamplitude of the detected signal is measured for each actuationamplitude. In another actuation scheme, the resonator is actuated with asinusoidal signal of varying amplitude and the corresponding amplitudeof the detected signal is related to the parameters of a model for anon-Newtonian fluid. All such activation schemes and measured propertiesof the detected signal are within the scope of this disclosure.

In some aspects, the non-linear response of a resonator in anon-Newtonian fluid is such that the resonator can produce harmonics ofthe actuation frequency. For example, if the resonator is actuated at agiven frequency, the detected motion will contain energy at theactuation frequency as well as energy at harmonics or multiples of theactuation frequency, for example at twice the actuation frequency.Accordingly, the parameters of a model describing the non-Newtonianshear stress versus strain rate characteristic of a fluid can bedetermined by measuring in the detected signal, for example, theamplitudes and phases of the fundamental and harmonics of the actuationfrequency. All such actuation schemes and measured properties of thedetected signal are within the scope of this disclosure.

In some aspects, if two frequencies are present in the actuation signal,the non-linear dynamics of the resonator in a non-Newtonian fluid canproduce sum and difference frequencies in the response of the resonatorand that the amplitudes and phases of the sum frequency or differencefrequency can be related to parameters of a model describing thenon-Newtonian rheology of the fluid. All such actuation schemes andmeasured properties of the detected signal are within the scope of thisdisclosure.

In example implementations, the relative phase between the drive signalcontrolling the actuator 115 and the measured signal from the detector120 is monitored as the amplitude of the drive signal is varied. Througha spectral analyzer system, for example, the in-phase and out-of-phasecomponents of the signal from the detector relative to the signalcontrolling the actuator can then be obtained and used to determinerheological properties such as the storage and viscous moduli. Thefrequency of the actuation signal (for example, signal controlling theactuator) may also be varied parametrically around a bandwidth ofinterest, where a resonant peak for any given vibrational mode mayexist. The amplitude and phase of the output signal may then be obtainedwith or by a spectral analyzer system, as mentioned previously, and thetransfer function of the system may then be obtained and fitted to theappropriate mathematical model including the shear-dependent damping(for example, viscosity). For example, depending on the geometry of theresonator 105, a spatial distribution of shear-rates may be inducedaround the vibrating body of the resonator as the fluid is displaced anddeformed. Through mathematical or computational modeling, the measuredtransfer function including a damping force model related to a specificrheological model can be used to extract the rheological parameters ofthe fluid. Alternatively, a multi-parametric study can also beperformed, where a complex input signal containing a plurality ofcomponents with different frequencies, amplitudes, and phases may beused to drive the resonator. For example, by using two sinusoidalsignals near one of the resonant modes of the detector 120, acharacteristic harmonic distortion in the oscillatory output signal maybe obtained due to nonlinear changes in the viscous dissipative forcesfrom the fluid. The resonator 105 can then be operated at a particularrange or variety of frequencies and measuring the induced harmonicdistortion within a certain bandwidth. The obtained spectra may then berelated to the rheological profile of the device by appropriatemathematical or computational modeling.

The decay envelope measurement technique can be used when the resonator105 is actuated to oscillate at a determined amplitude and, after astable oscillation is established, the drive signal is removed allowingthe amplitude of oscillation to decay. Deviations from a pureexponential decay in the decay envelope can then be used to obtainparameters of a model describing a non-Newtonian fluid. Relating themeasured characteristics of the detected motion of the resonator toparameters of a rheological model for the non-Newtonian fluid can beaccomplished by applying the selected actuation scheme, collectingmeasured characteristics of the detected resonator motion fornon-Newtonian test fluids for which the parameters of a rheologicalmodel are known, and using, for example, non-linear statisticalregression to establish an equation relating the parameters to themeasured characteristics. Alternatively, the measured characteristicsand associated model parameters can be organized as a lookup table,where interpolation (for example, linear interpolation, or splineinterpolation) are used to find interpolated model parameters based onhow close the measured characteristics for an unknown sample are to themeasured characteristics for one or more test fluids.

The actuator is, in some examples, a transducer that converts anelectrical signal into a mechanical property at the resonator, such as adisplacement, a velocity, an acceleration, a strain, a stress, or aforce, proportional in magnitude to the electrical signal. Suchtransducers include, but are not limited to: a piezoelectric crystal, asolenoid, a magneto-strictive material, a linear motor comprising a coilthat produces a magnetic field and a permanent magnet that experiences aforce in response to the field, and a capacitive actuator where anelectric field produces a force between charged electrodes. The detectoris preferentially a transducer that converts a mechanical property atthe resonator, such as a displacement, a velocity, an acceleration, astrain, a stress, or a force to an electrical signal, proportional inmagnitude to the mechanical property Such transducers include, but arenot limited to: a piezoelectric element, a capacitive sensor, aninductor with a core attached to the resonator, a piezoresistiveelement, a strain sensor, a force sensor, a pressure sensor, a linearvariable differential transformer, a linear variable inductance sensor,a magnetostrictive element, and a photodetector.

FIG. 3 is flowchart that describes an example implementation of a method300 for determining rheological properties of a fluid sample. Method300, for example, may describe an example operation of or with therheological property measurement system 200 shown in FIG. 2 . Forexample, one or more steps of method 300 may be executed by or with thecontrol system 210 of the rheological property measurement system 200.

Method 300 may begin at step 302, which includes operating a mechanicalresonator disposed in a volume that contains a fluid sample. Forexample, the control system 210 may actuate the mechanical resonator 206(for example, a resonator, or mechanical resonator, such as apiezoelectric crystal, a MEMS device, or any vibrating device) while theresonator 206 is disposed in the volume of fluid sample 204. The controlsystem 210 may actuate the resonator 206 by, for example, capacitive,piezoelectric, magnetic, optical or any other physical signal orcombination of signals to induce harmonic or anharmonic motion of theresonator 206 in the fluid sample 204.

The resonator is comprised of a mechanical structure which supportsvibrations and may include intrinsically or extrinsically the actuatorand/or detector of said vibrations. It may be fabricated by traditionalsubtractive machining processes through milling, drilling, turning, orother machine-aided processes, manual or automatic. It may be comprisedof any material able to support vibrations on the machined mechanicalstructure such as metals, silicon, silicon-nitride, quartz lithiumniobite, silicon carbide, or any other crystal, natural material, oralloy compatible with said machining processes. The mechanical structuremay be fabricated into any shape such as cantilevers, beams, wires,plates, tuning forks, or any other geometry able to produce flexural,torsional or bulk mechanical vibrations. Other fabrication methods maybe additive, which can also include “additive manufacturing,” or3D-printing. These may be used to fabricate the mechanical structure orto add function or features to the mechanical structure such as, but notlimited to, actuation capabilities, or detection capabilities.Furthermore, these functions or features may be added via commerciallyavailable components such as strain gauges, piezoelectric elements,magnets, external coils, pressure or acoustic sensors, accelerometers,lasers, or photodetectors. The fabrication process may include, in partor in total, micro or nanomachining steps such as optical lithography,electron beam lithography, soft lithography, film deposition, physicalor chemical evaporation techniques, etching processes, bonding, or otherbottom-up or top-down micro/nano assembly or patterning techniques.These may be used to fabricate any or the total of the componentsincluding the mechanical structure, actuators, or detectors. Themechanical structure, actuators, and/or detectors may be of sizesspanning the nanometer scale to macroscopic sizes. The mechanicalstructure size and stiffness may therefore span a large band ofvibrational modes with frequencies from Hertz to tens or hundreds ofmegahertz for flexural and torsional resonators, and up to gigahertzfrequencies for bulk-mode resonators.

Step 302 may also include establishing or implementing (or both) anactuation protocol of the mechanical resonator 206 in which theresonator 206 is set either in steady-state motion or is controlled tovibrate through a time sequence of displacements at various amplitudesor frequencies that would induce a predictable (theoretically orcomputationally) spatial distribution of deformations (or deformationhistory) on the fluid sample 204 at any given time. Thus, there may be ameasurable change of the motion of the mechanical resonator 206 inducedand, thereby, inducing a measurable change on the motion of the devicedue to the changes in the properties of the fluid from saiddeformations.

The motion of the resonator may be periodic or non-periodic. Periodicmotion may include harmonic and an-harmonic motion of single or multiplefrequency components as well as quasi-periodic motion at incommensurablefrequencies. Non-periodic motion may include at least one component ofthe motion that cannot be represented by a periodic function, such asthe exponential envelope of an exponentially decaying or growingoscillatory signal.

The frequency or frequencies of motion of the resonator may be chosen ordesigned (via stiffness or size) according to the viscoelasticcharacteristics of the fluid whereby the response measured by theresonator may be more affected by either viscous or elastic componentsof the fluid above or below a characteristic fluid relaxation time, orrelaxation time spectra, as determined by the fluid's specificmicrostructural characteristics.

In some aspects, mechanical properties of the particular mechanicalresonator 206 can be described (for instance, in the Butterworth-VanDyke model) as a resonant inductive-capacitive-resistive (LCR) circuit.At resonance, the capacitive (C) and inductive (L) parts of the circuitmay cancel out, leaving only a resistive (R) component. Thus, a measuredcurrent amplitude (I) and the driving voltage (V), corresponding to thevelocity and the driving force in the mechanical domain, scale linearlyaccording to:

${I = {\left( \frac{1}{R} \right)V}},$

when the resistance (equivalent to the damping in the mechanical domain)is constant. Changes in the damping as a function of excitationamplitude indicate changes in the viscosity of the fluid, since thedamping coefficient is dependent on geometrical parameters of themechanical resonator 206 and the viscosity of the fluid sample 204.

Turning briefly to FIG. 4 , this figure shows a graph 400 thatillustrates an example of linear dependence of measured current as afunction of excitation amplitude in a mechanical resonator that is usedin the process of FIG. 3 . Graph 400 includes an x-axis 402 that showsdrive voltage in millivolt (mV) and a y-axis 404 that shows amplitude innanoamperes (nA). Plotted points 406 represent measured current versusexcitation voltage for the mechanical resonator 206 (for example, apiezoelectric tuning fork device) in vacuum. Graph 400 also includes afitted curve 408 according to the plotted points 406 that separate ashear thinning region and a shear thickening region, as shown.

In graph 400, the resistive component (R) represents the dominantconstant damping from the intrinsic mechanical properties of theresonator 206 since it is in vacuum. When the mechanical resonator 206is immersed in the fluid sample 204,R=R _(i) +R _(fluid),

where R_(i) and R_(fluid) represent the intrinsic and the fluid damping,respectively. When the fluid environment is a liquid (such as fluidsample 204), the R_(fluid) dominates the damping and R_(i) can beignored. In this case, at large excitations, deviations from lineardependence would indicate either shear thinning or shear thickening, asillustrated in graph 400. The rate of deviation of the damping couldthen be represented as a power law of the such thatR(v)˜μ(v)˜v ^(α),

where μ(v) represents viscosity, v is the velocity of oscillation, and αis a constant coefficient. The damping force, F_(D), on the mechanicalresonator 206 can then be expressed as:F _(D) =c ₀μ(v)v=c ₀μ₀ v ^(1+α),

where c₀ and μ₀ represent the geometrical and viscous factors in thelinear regime. By analytical or computational means, the fluid structureinteraction (stress and fluid velocity distribution around the movingresonator 206), depending on the geometry of the resonator 206, wouldallow the conversion of damping force versus velocity to shear stress(σ(γ)) versus shear rate ({dot over (γ)}) such that a constitutiveequation can be written and a rheological model (for example, to use instep 306) can be constructed.

Method 300 may continue at step 304, which includes measuring at leastone motion characteristic of the vibrating mechanical resonator. Forexample, the control system 210 may operate the laser beam source 212 togenerate a laser beam (for example, a HeNe laser beam) that passes overthe beam splitter 214 to reflect a portion to the photodetector 216 anda portion toward the mechanical resonator 206. In some aspects, a motioncharacteristic of the vibrating resonator 206 may be measured viacapacitive, piezoelectric, magnetic, optical or any other transductiondomain that provides a measurable signal from the motion of themechanical resonator 206. In some aspects, the motion characteristic maybe one or more of a velocity or displacement amplitude of the resonator206, a phase of the resonator 206, or any characteristic of the motion,or (linear or nonlinear) combination of motions, of the mechanicalresonator 206, in time or frequency domain, as induced by the actuationprotocol of the resonator 206 by the control system 210.

Method 300 may continue at step 306, which includes comparing themeasured motion characteristic with a specified rheological model. Forexample, the rheological model may be a mathematical or a computationalmodel that predicts a change in one or more motion characteristics ofthe fluid sample 204 according to a deformation amplitude (oramplitudes) and a deformation rate (or rates) induced in the fluidsample 204. The chosen rheological model may also account for, forexample, the known geometry of the mechanical resonator 206, and theimposed actuation protocol.

In some aspects, when the mechanical resonator 206 is actuated byelectrical or magnetic means and vibrated in a Newtonian fluid, it willexperience a damping force that is proportional to the instantaneousvelocity of the resonator 206. When the mechanical resonator 206 isvibrated in a non-Newtonian fluid (such as, in some aspects, fluidsample 204), this damping force is related to the velocity of theresonator 206 in a non-linear way. For example, in non-Newtonian fluids,the damping force may increase or decrease relative to the linear trend.A fluid where the damping force grows above the linear trend at largevelocity is called a “shear-thickening” fluid and if the damping forcedecrease below the linear trend at large velocity the fluid is called“shear-thinning.” Rheological models, such as the Hershel-Bulkley model,may describe this non-linear dependence of damping force on velocity innon-Newtonian fluids. The Hershel-Bulkley model is:σ=σ₀ +k{dot over (γ)} ^(n),

where σ is the shear stress, σ₀ is the yield stress, {dot over (γ)} isthe shear rate, k is the consistency index, and n is the flow index.Fluids described by this relation are yield-stress fluids. When anobject moves in a yield-stress fluid, a minimal force which depends onthe cross sectional area of the resonator 106 and the yield stress (σ₀)is applied to start the motion:F _(D) =αL ²σ₀,

where L is the characteristic size of the resonator 206 and α is aconstant that indicates that the relevant deformation for yieldingextends beyond the surface of the resonator 206. When the resonator 206is set in motion, an additional velocity dependent component to thedamping force is added such that:

${F_{D} = {\alpha{L^{2}\left\lbrack {\sigma_{0} + {k\left( \frac{v}{l} \right)}^{n}} \right\rbrack}}},$

where l represents a length-scale which defines the fluidized regionbounded by the un-yielded region in the fluid sample 204.

Method 300 may continue at step 308, which includes determining one ormore rheological properties of the fluid sample based on the comparison.For example, in some aspects, the rheological properties of one or moreof complex viscosity, storage modulus (G′), loss modulus (G″), as wellas steady state shear properties such as apparent viscosity, flow index,and consistency factor may be determined in step 308. In some aspects,the comparison includes iteratively determining, via nonlinear fitting,inversion, or optimization, the rheological parameters of the chosenrheological model that best describe the measured motion characteristicsof the motion of the mechanical resonator 206.

In some aspects, step 308 includes an inversion analysis, in which boththe solid characteristics of the mechanical resonator 206 andnon-Newtonian fluid characteristics of the fluid sample 204 (and theirinteraction) into account. In such aspects, it may be assumed that themechanical resonator 206 is fully immersed in the fluid sample 204, andalso that motion of the resonator 206 may not be influenced by thepresence of boundary or free surface to simplify the inversion analysis.The solid side is driven by a forcing mechanism into a motion and themotion can be modelled as:mÿ+c _(s)({dot over (y)}){dot over (y)}+ky=F(t)+R(t),

where m is a mass of moving part (the resonator 106), c_(s) is astructural damping, k is a spring constant, F(t) is the driving force,and R(t) is the reaction force to the mass from surrounding fluid.Assuming that the resonator 106 is moved in a vacuum or thin air, R(t)is negligibly small and can be set to zero. In a highly viscous media,R(t) can make the system underdamped, leading to no oscillation of theresonator 106. R(t) is computed from the stress field in the fluid, moreprecisely on the solid surface.

The reaction force R(t) is composed of a pressure term and a viscousterm. For example, in a Newtonian fluid:

${{R_{i}(t)} = {= {{\int{\sigma_{ij}n_{j}dS}} = {{\int{\left( {{{- p}\delta_{ij}} + \tau_{ij}} \right)n_{j}dS}} = {\int{\left( {{{- p}\delta_{ij}} + {v\left( {\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}} \right)}} \right)n_{j}dS}}}}}},$

where the integration is done over a closed surface, p is pressure,δ_(ij) is the Kronecker delta, v is viscosity, τ_(ij) is shear stress,and n_(j) is the unit vector normal to the surface pointing toward thesolid (the resonator 206). The first term explains the reaction forcedue to the pressure and the second term is due to the friction betweenthe resonator 106 and the fluid sample 204. The fluid side can bedescribed by the Cauchy equation with a non-Newtonian constitutiveequation:

${{\frac{\partial\rho}{\partial t} + {{\nabla \cdot \rho}u}} = 0},$

${{\rho\left( {\frac{\partial u}{\partial t} + {u \cdot {\nabla u}}} \right)} = {{\nabla \cdot \sigma} = {{- {\nabla p}} + {\nabla \cdot \tau}}}},$

where σ is the stress tensor, and can be related to fluid velocity, u.Non-Newtonian fluid models include Bingham and power-law fluids. Forexample, the power-law fluid relates τ with velocity, u, using twoparameters K and n:

$\tau_{ij} = {K\left( \frac{\partial u_{i}}{\partial x_{j}} \right)}^{n}$

When a rheological model is chosen, then the parameters in the model maybe initially unknown. Since these parameters may not be directlyobservable, they can be estimated using an inversion framework. Theinversion framework may include a deterministic approach that minimizesdifferences between observed measurements and predicted measurementsusing the selected rheological model and initial parameter values.Specifically, measurements of displacement (y_(o)) or velocity ({dotover (y)}_(o)) may be taken in step 304 (or at a previous step prior tomethod 300). Using the selected rheological model, fluid-structureinteraction may be simulated, and the simulation gives correspondingmodeled quantities, either displacement (y_(m)) or velocity ({dot over(y)}_(m)), where subscripts, o and m, are the initials of observed andmodelled, respectively. The optimization (for example, minimization)problem to solve is:J(p ₁ ,p ₂ ,p ₃, . . . )=∫|y _(o) −y _(m)(p ₁ ,p ₂ ,p ₃, . . . )|² dt,

where (p₁, p₂, p₃, . . . ) are parameters for a rheological model. Theexample optimization problem is a partial differential equation(PDE)-constrained nonlinear optimization problem that usesregularization terms for stable solution. Computationally, suchoptimization problems incur many iterations and forward modellings. Theoptimal solution of the optimization problem is the set of rheologicalparameters that best explain the measured motion characteristics of themechanical resonator 206 in the fluid sample 204.

In an example experiment performed with a system such as rheologicalproperty measurement system 200, a fluid sample of laponite gel as thefluid sample 204. A piezoelectric crystal tuning fork resonator was usedas the mechanical resonator 106, which was actuated by a sinusoidalsignal from an external alternating current (AC) signal generator (notshown in FIG. 2 ). The output of the signal generator was furtheramplified by a 50X power amplifier in order to generate peak-to-peakvoltages above 10 Volts (V). Due to the large excitation voltages andthe parasitic capacitance from the piezoelectric crystal, a directelectrical detection of the induced current from the piezoelectricfork's motion was difficult without overloading the detection circuitry.Instead, motion of the resonator was measured optically using the knifeedge technique as described with reference to FIG. 2 .

A HeNe laser was used as laser beam source 212 and was focused at theedge of a reflective area (metal electrode) on one of the fork's movingprongs, letting half of the laser beam reflect towards a photodetector(216) and the other half transmit through the crystal (resonator 206).This way, as the prong of the fork moved, the intensity of the light wasmodulated, since the edge of the reflective surface also moves toreflect more or less light during a half period of oscillation. Theinduced current from the light collected was then a periodic function ofthe amplitude of oscillation.

This current was then amplified by a current-to-voltage converter andfed into a lock-in amplifier for phase sensitive detection. Thereference signal is directly fed from the TTL output of the AC signalgenerator used to actuate the fork.

In the example experiment, the tuning fork resonator was tested with theabove described technique in laponite gel, a model yield-stress fluidsimilar to typical drilling fluids which is also optically transparent.A mixture of 200 grams of deionized water, 4 grams of laponite and 0.25grams of sodium hydroxide comprised the fluid sample (204). Whenimmersed in the fluid, a frequency sweep was performed on the tuningfork and resonance peaks were obtained at various excitation voltages asshown in FIG. 5 .

Turning briefly to FIG. 5 , this figures shows a graph 500 thatillustrates optically detected resonance peaks for a mechanicalresonator immersed in a fluid sample during an experiment according tothe process of FIG. 3 . As shown in FIG. 5 , graph 500 includes anx-axis 502 of scanned frequency in Hertz and a y-axis 504 of voltageamplitude in volts. Curves 506, 508, and 510 represent excitationvoltages of 140 V, 50 V, and 100 V, respectively.

Further, FIG. 6 is a graph 600 that illustrates peak amplitude atresonance for the mechanical resonator immersed in the fluid sampleduring the experiment according to the process of FIG. 3 . Graph 600includes an x-axis 602 that represents excitation voltage (in volts) anda y-axis 604 that represents peak amplitude at resonance of the tuningfork (in volts). The measured points 606 are shown, as well as a curve608 fit to a linear portion of the points 606. Here, the peaks werenormalized by the excitation voltages. The peak amplitude was extractedby fitting the obtained resonance peak to a model function. As afunction of excitation voltage, the amplitude is seen to increaselinearly up to 100 V and then begins to deviate (non-linearly).

FIG. 7 is a schematic illustration of an example controller (or controlsystem) 700 for a rheological property measurement system, such as thecontrol system 210 for rheological property measurement system 200. Thecontroller 700 is intended to include various forms of digitalcomputers, such as printed circuit boards (PCB), processors, or digitalcircuitry. Additionally the system can include portable storage media,such as, Universal Serial Bus (USB) flash drives. For example, the USBflash drives may store operating systems and other applications. The USBflash drives can include input/output components, such as a wirelesstransmitter or USB connector that may be inserted into a USB port ofanother computing device.

The controller 700 includes a processor 710, a memory 720, a storagedevice 730, and an input/output device 740. Each of the components 710,720, 730, and 740 are interconnected using a system bus 750. Theprocessor 710 is capable of processing instructions for execution withinthe controller 700. The processor may be designed using any of a numberof architectures. For example, the processor 710 may be a CISC (ComplexInstruction Set Computers) processor, a RISC (Reduced Instruction SetComputer) processor, or a MISC (Minimal Instruction Set Computer)processor.

In one implementation, the processor 710 is a single-threaded processor.In another implementation, the processor 710 is a multi-threadedprocessor. The processor 710 is capable of processing instructionsstored in the memory 720 or on the storage device 730 to displaygraphical information for a user interface on the input/output device740.

The memory 720 stores information within the controller 700. In oneimplementation, the memory 720 is a computer-readable medium. In oneimplementation, the memory 720 is a volatile memory unit. In anotherimplementation, the memory 720 is a non-volatile memory unit.

The storage device 730 is capable of providing mass storage for thecontroller 700. In one implementation, the storage device 730 is acomputer-readable medium. In various different implementations, thestorage device 730 may be a floppy disk device, a hard disk device, anoptical disk device, a tape device, flash memory, a solid state device(SSD), or a combination thereof.

The input/output device 740 provides input/output operations for thecontroller 700. In one implementation, the input/output device 740includes a keyboard or pointing device (or both). In anotherimplementation, the input/output device 740 includes a display unit fordisplaying graphical user interfaces.

The features described can be implemented in digital electroniccircuitry, or in computer hardware, firmware, software, or incombinations of them. The apparatus can be implemented in a computerprogram product tangibly embodied in an information carrier, forexample, in a machine-readable storage device for execution by aprogrammable processor; and method steps can be performed by aprogrammable processor executing a program of instructions to performfunctions of the described implementations by operating on input dataand generating output. The described features can be implemented in oneor more computer programs that are executable on a programmable systemincluding at least one programmable processor coupled to receive dataand instructions from, and to transmit data and instructions to, a datastorage system, at least one input device, and at least one outputdevice. A computer program is a set of instructions that can be used,directly or indirectly, in a computer to perform a certain activity orbring about a certain result. A computer program can be written in anyform of programming language, including compiled or interpretedlanguages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment.

Suitable processors for the execution of a program of instructionsinclude, by way of example, both general and special purposemicroprocessors, and the sole processor or one of multiple processors ofany kind of computer. Generally, a processor will receive instructionsand data from a read-only memory or a random access memory or both. Theessential elements of a computer are a processor for executinginstructions and one or more memories for storing instructions and data.Generally, a computer will also include, or be operatively coupled tocommunicate with, one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as erasable programmableread-only memory (EPROM), electrically erasable programmable read-onlymemory (EEPROM), solid state drives (SSDs), and flash memory devices;magnetic disks such as internal hard disks and removable disks;magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor andthe memory can be supplemented by, or incorporated in, ASICs(application-specific integrated circuits).

To provide for interaction with a user, the features can be implementedon a computer having a display device such as a CRT (cathode ray tube)or LCD (liquid crystal display) or LED (light-emitting diode) monitorfor displaying information to the user and a keyboard and a pointingdevice such as a mouse or a trackball by which the user can provideinput to the computer. Additionally, such activities can be implementedvia touchscreen flat-panel displays and other appropriate mechanisms.

The features can be implemented in a control system that includes aback-end component, such as a data server, or that includes a middlewarecomponent, such as an application server or an Internet server, or thatincludes a front-end component, such as a client computer having agraphical user interface or an Internet browser, or any combination ofthem. The components of the system can be connected by any form ormedium of digital data communication such as a communication network.Examples of communication networks include a local area network (“LAN”),a wide area network (“WAN”), peer-to-peer networks (having ad-hoc orstatic members), grid computing infrastructures, and the Internet.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed, but rather as descriptions of features specific to particularimplementations. Certain features that are described in thisspecification in the context of separate implementations can also beimplemented in combination in a single implementation. Conversely,various features that are described in the context of a singleimplementation can also be implemented in multiple implementationsseparately or in any suitable subcombination. Moreover, althoughfeatures may be described as acting in certain combinations and eveninitially claimed as such, one or more features from a claimedcombination can in some cases be excised from the combination, and theclaimed combination may be directed to a subcombination or variation ofa subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the implementations described should not be understood asrequiring such separation in all implementations, and it should beunderstood that the described program components and systems cangenerally be integrated together in a single software product orpackaged into multiple software products.

Example Implementations

FIG. 2 is a schematic illustration of a specific implementation of therheological property measurement system 100. FIG. 2 shows a rheologicalproperty measurement system 200 that includes a fluid sample enclosure202 that can contain or hold a fluid sample 204. Disposed in theenclosure 202 is a mechanical resonator 206 (for example, a resonator)that is in contact with the fluid sample 204. Example implementations ofthe mechanical resonator 206 include a micro-electro-mechanical system(MEMS) or a piezoelectric flexural resonator (or other piezoelectricvibrating device). Further example include a tuning fork (for example, apiezoelectric crystal tuning fork resonator) that may be actuated byelectrical or magnetic energy. In this example, the mechanical resonator206 is fully immersed in the fluid sample 204.

The rheological property measurement system 200 also includes a laserbeam source 212 (for example, an actuator) that is positioned togenerate a laser beam 209 toward the mechanical resonator 206. In thisexample implementation, the laser beam source 212 is a helium-neon (or“HeNe”) laser beam source that generates a HeNe laser beam. In thisexample, the laser beam 209 is directed across a beam splitter 214 thatis positioned between the laser beam source 212 and the mechanicalresonator 206. Thus, the rheological property measurement system 200uses the knife-edge technique in which the laser beam 209 is split bythe beam splitter 214, and a split portion 213 of the laser beam 209 isreflected toward the photodetector 216, while another split portion 205of the laser beam 209 is directed toward the mechanical resonator 206. Areflected portion 207 of the split portion 205 of the laser beam 209reflects back toward the beam splitter 214.

The photodetector 216 (for example, a detector) of the exampleimplementation of the rheological property measurement system 200 ispositioned to receive the split portion 213 of the laser beam 209 fromthe beam splitter 214. Generally, the photodetector 216, through receiptof the split portion 213 of the laser beam 209, measures an intensity ofthe light from the beam that modulates due to vibration of themechanical resonator 206. This intensity is converted, by thephotodetector 216, into a current magnitude (which may be used asdescribed later to determine one or more motion characteristics of themechanical resonator 206).

In some implementations, the fluid sample 204 is a static fluid sample.In other words, the fluid sample 204 is not moving (or isinsignificantly moving) during operation of the mechanical resonator206. In an alternative implementation, a flow 217 of the fluid sample204 may be circulated through conduit 208 and to the fluid sampleenclosure 202. In some aspects, a pump 220, a valve 218, or both, may beused to control the flow 217 of the fluid sample 204 into (and out of)the fluid sample enclosure 202. In some aspects, operation of therheological property measurement system 200 may proceed whether thefluid sample 204 is static or moving, provided that a velocity of themoving fluid sample 204 may need to be such that accurate rheologicalproperties can be determined of the moving sample.

As shown, the example implementation of the rheological propertymeasurement system 200 includes a control system 210 (for example, acontroller) that is communicably coupled to at least the mechanicalresonator 206, the laser beam source 212, the photodetector 216, thevalve 218 and the pump 220. In some aspects, the control system 210 is astand-alone control system (for example, a hardware computerprocessor-based control system) that controls such components and mayalso send data, receive data, or both, to and from such components.Alternatively, control system 210 may represent multiple control systemsor controllers, each of which is specifically associated with, forexample, the mechanical resonator 206, the laser beam source 212, thephotodetector 216, the valve 218 and the pump 220.

As shown, the control system 210 includes or is communicably coupled toa database 221 that stores, for example, one or more predefinedrheological models 223. Each of the rheological models 223, in someaspects, is a numerical or computational model that associatesrheological properties of a particular fluid (for example, a particularliquid sample) with one or more measured characteristics of theparticular fluid. Examples of rheological models include a BinghamPlastic model, a power law model, a Hershel-Bulkley model, or a Carreaumodel.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the disclosure. For example, exampleoperations, methods, or processes described herein may include moresteps or fewer steps than those described. Further, the steps in suchexample operations, methods, or processes may be performed in differentsuccessions than that described or illustrated in the figures.Accordingly, other implementations are within the scope of the followingclaims.

What is claimed is:
 1. A method for determining rheological propertiesof a fluid, comprising: actuating a resonator disposed in a volume thatcontains a fluid sample to operate the resonator in the fluid sample ata predetermined actuation scheme; actuating the resonator with anactuation protocol that actuates the resonator in at least one of asteady state motion or a time-dependent motion, wherein actuating theresonator with an actuation protocol comprises inducing a measurablechange on a motion of the resonator based at least in part due to one ormore deformations in the fluid sample; measuring, with a photodetectorpositioned to receive a reflected laser beam that originates with alaser beam source and reflects from the operating resonator, at leastone response characteristic of the resonator based on the operation ofthe resonator in the fluid sample; comparing the at least one measuredresponse characteristic to a rheological model that associates the atleast one response characteristic of the resonator to one or morerheological properties of the fluid sample; and based on the comparison,determining one or more rheological properties of the fluid sample. 2.The method of claim 1, wherein the resonator comprises a mechanicaloscillator.
 3. The method of claim 2, wherein the mechanical oscillatorcomprises a piezoelectric crystal, a cantilever beam, a MEMS device, atorsional spring, a vibrating wire, or a tuning fork.
 4. The method ofclaim 3, wherein the fluid sample comprises a non-Newtonian liquid. 5.The method of claim 4, wherein the non-Newtonian liquid comprises ahydrocarbon liquid, a completion liquid, or a petroleum-derived liquid.6. The method of claim 1, wherein actuating the resonator comprisesactuating motion on the resonator through one or more signals to induceharmonic or anharmonic motion.
 7. The method of claim 6, wherein the oneor more signals comprises one or more capacitive, piezoelectric,magnetic, or optical signals.
 8. The method of claim 1, wherein thetime-dependent motion comprises at least one sequence of displacementsof the resonator with at least one of a plurality of amplitudes orfrequencies.
 9. The method of claim 1, wherein measuring at least oneresponse characteristic of the resonator comprises measuring at leastone response characteristic in a transduction domain that provides ameasurable signal from the operation of the resonator.
 10. The method ofclaim 9, wherein measuring at least one response characteristic in atransduction domain that comprises at least one of a capacitive, apiezoelectric, a magnetic, or an optical characteristic.
 11. The methodof claim 1, wherein measuring at least one response characteristic ofthe resonator comprises measuring at least one of a velocity or adisplacement of amplitude or phase of the resonator in at least one of atime domain or a frequency domain.
 12. The method of claim 1, whereincomparing the at least one measured response characteristic to arheological model comprises comparing at least one motion responsecharacteristic of the resonator to at least one of a mathematical modelor a computational model.
 13. The method of claim 12, wherein the atleast one of the mathematical model or the computational model relates achange in the at least one motion response characteristic to at leastone of a deformation amplitude or a deformation rate induced in thefluid sample.
 14. The method of claim 1, wherein actuating the resonatordisposed in the volume that contains the fluid sample to operate theresonator in the fluid sample at the predetermined actuation schemecomprises actuating a mechanical oscillator disposed in the volume thatcontains the fluid sample to vibrate the mechanical oscillator in thefluid sample at a predetermined vibration protocol.
 15. The method ofclaim 14, wherein measuring the at least one response characteristic ofthe resonator based on the operation of the resonator in the fluidsample comprises measuring at least one motion response characteristicof the mechanical oscillator based on a non-linear response of themechanical oscillator in the fluid sample.
 16. The method of claim 15,wherein comparing the at least one measured response characteristic to arheological model that associates characteristics of the fluid sample toone or more rheological properties comprises comparing the at least onemeasured motion response characteristic to the rheological model thatassociates motion characteristics of the fluid sample to one or morerheological properties.
 17. The method of claim 15, wherein measuringthe at least one motion response characteristic of the mechanicaloscillator comprises measuring the at least one motion responsecharacteristic with the photodetector positioned to receive thereflected laser beam that originates with the laser beam source andreflects from the vibrating mechanical oscillator.
 18. The method ofclaim 1, further comprising circulating the fluid sample into the volumeduring actuation of the resonator.
 19. The method of claim 1, whereindetermining one or more rheological properties of the fluid samplecomprises iteratively determining the one or more rheological propertiesof the fluid sample with a numerical inversion or optimization protocol.20. The method of claim 1, wherein the one or more rheologicalproperties comprises at least one of a complex viscosity, a storagemodulus, a loss modulus, an apparent viscosity, a flow index, or aconsistency factor of the fluid sample.
 21. The method of claim 1,wherein the rheological model comprises at least one of a BinghamPlastic model, a power law model, a Hershel-Bulkley model, or a Carreaumodel.
 22. The method of claim 1, wherein the fluid sample comprises anon-Newtonian liquid.
 23. The method of claim 22, wherein thenon-Newtonian liquid comprises a hydrocarbon liquid, a completionliquid, or a petroleum-derived liquid.